swerve wrote:
In the figure shown above, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?
A. 4
B. 3
C. 2
D. \(\sqrt{3}\)
E. \(\sqrt{2}\)
Smaller circle:
Let r=1.
Area = πr² = π(1²) = π
Circumference = 2πr = 2π(1) = 2π
Since the area of the shaded region is 3 times the area of the smaller circle, the shaded region = 3π.
Larger circle:
Area = (smaller circle) + (shaded region) = π + 3π = 4π.
Thus:
πr² = 4π
r = 2
Circumference = 2πr = 2π(2) = 4π
The circumference of the larger circle is how many times the circumference of the smaller circle?
(larger circumference)/(smaller circumference) = 4π/2π = 2
The correct answer is
C.
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